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Right Triangle on Parabola

Source: AMC 12 2008B Problem 17

February 29, 2008
conicsparabolageometryanalytic geometrycalculusgraphing linesslope

Problem Statement

Let A A, B B, and C C be three distinct points on the graph of y\equal{}x^2 such that line AB AB is parallel to the x x-axis and △ABC \triangle{ABC} is a right triangle with area 2008 2008. What is the sum of the digits of the y y-coordinate of C C? <spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 17<spanclass=′latex−bold′>(C)</span> 18<spanclass=′latex−bold′>(D)</span> 19<spanclass=′latex−bold′>(E)</span> 20 <span class='latex-bold'>(A)</span>\ 16 \qquad <span class='latex-bold'>(B)</span>\ 17 \qquad <span class='latex-bold'>(C)</span>\ 18 \qquad <span class='latex-bold'>(D)</span>\ 19 \qquad <span class='latex-bold'>(E)</span>\ 20
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